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A157938
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Numbers n divisible by the least prime >= sqrt(n) but not by the largest prime <= sqrt(n).
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3
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10, 20, 28, 42, 55, 66, 88, 99, 110, 130, 156, 170, 187, 204, 238, 255, 272, 304, 342, 368, 391, 414, 460, 483, 506, 551, 580, 609, 638, 696, 725, 754, 783, 812, 868, 930, 962, 999, 1036, 1073, 1110, 1184, 1221, 1258, 1295, 1332, 1394, 1435, 1476, 1558
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OFFSET
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1,1
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COMMENTS
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Also: Numbers n divisible by the least prime >= sqrt(n) which are not in A001248 (primes squared) or A006094 (product of two consecutive primes). A subsequence of A157937.
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LINKS
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FORMULA
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EXAMPLE
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a(1)=10 and a(2)=20 are divisible by 5 = nextprime(sqrt(10)) = nextprime(sqrt(20)) and neither a prime squared (as are 4 and 9) nor product of consecutive primes (as are 6 and 15).
5,7,8 are not in this sequence, since not a multiple of 3=nextprime(sqrt(5))=nextprime(sqrt(8)).
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MATHEMATICA
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dpQ[n_]:=Module[{srn=Sqrt[n], a, b}, a=If[PrimeQ[srn], srn, NextPrime[ srn]]; b=If[PrimeQ[srn], srn, NextPrime[srn, -1]]; Divisible[n, a]&& !Divisible[ n, b]]; Select[Range[2000], dpQ] (* Harvey P. Dale, Oct 10 2011 *)
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PROG
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(PARI) for( n=5, 1999, n % nextprime(sqrtint(n-1)+1) & next; n % precprime(sqrtint(n)) & print1(n", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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